Inductor for radio frequency integrated circuit

ABSTRACT

An inductor used in a radio frequency integrated circuit is disclosed. The inductor includes a plurality of unit inductors each having a vertical spiral structure, wherein a vertical cross-section of at least one unit inductor selected from the plurality of unit inductors is an inverted trapezoid.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to an inductor. More particularly,the present invention relates to an inductor used in a radio frequencyintegrated circuit (RFIC), and which has a multi-layer structure on thevertical and a spiral structure on the horizontal.

[0003] 2. Description of the Related Art

[0004] An inductor is a passive device generally used in an RFIC. Sincean inductor occupies the largest area in an RFIC, and is influenced byleakage of a substrate of the RFIC, it is difficult to obtain goodleakage current characteristics for the circuit, which results indeterioration of communication quality.

[0005] Inductors also operate as passive devices used for impedancematching in RFICSs, as high quality factors of resonance tanks (L-C)that are used in voltage controlled oscillators (VCOs), and areimportant in reducing phase noise. However, it is difficult tomanufacture an inductor having a high quality factor using acomplementary metal oxide semiconductor (CMOS) process because ofleakage of the substrate.

[0006] Accordingly, various methods of manufacturing inductors having ahigh quality factor have been studied. For example, an inductor having ahigh quality factor may be manufactured according to methods such asusing a high resistance substrate, forming a thick oxide layer on asubstrate to increase a gap between the substrate and the inductor,etching a substrate under an inductor after forming the inductor, andshielding a current from leaking into a substrate by forming a groundmetal layer on the substrate.

[0007] However, each of these methods for manufacturing inductorsrequires an additional CMOS process, thereby increasing the cost ofmanufacturing the inductors.

[0008] Meanwhile, considering that the manufacturing cost of an inductoris proportional to the area thereof, an inductor that occupies thelargest area in an RFIC according to the prior art presents a large costburden.

[0009] Inductance of an inductor may be increased by increasing the turnnumber of the inductor. However, when this method is used, the qualityfactor Q of the inductor is reduced due to conductivity loss, which,combined with an effect caused by coupling the inductor to a substrate,results in reduction of the resonance frequency of the inductor, andthus the utilization range of the inductor is reduced.

[0010] For example, in a spiral inductor manufactured using a 0.18 μmCMOS process and having a width of 15 μm, a gap of 1.5 μm between woundwirings, a conductor thickness of 2 μm, and an inside diameter of 60 μm,when a turn number, or number of times the wiring is wound, is 3.5, thequality factor Q of the inductor is 6.5 in a range of 2 GHz, theinductance is 3.8 nH, and the resonance frequency is 6 GHz. However,when the turn number is increased to 7.5, although the inductance isincreased to 17.6 nH, the quality factor Q is reduced to 2.5, and theresonance frequency is reduced to 3 GHz.

[0011] It is difficult to embody an inductor model fit for the physicaland structural characteristics of circuit design because of effects suchas coupling among conductive lines of the inductor, coupling of theconductive lines to a silicon substrate, and a lossy substrate.

[0012]FIG. 1 illustrates a general spiral inductor 10 used in an RFICand an equivalent circuit thereof. Referring to FIG. 1, referencecharacter L_(S) denotes the total inductance obtained by summing aself-inductance of the spiral inductor 10 and metal inductances amongmetal lines of the spiral inductor. Reference character R_(S) denotesthe total resistance obtained by summing a direct current (DC)resistance of the spiral inductor 10 and an alternating current (AC)resistance affected by an ultra radio frequency skin effect. Referencecharacter C_(S) denotes a parasitic capacitance of a parasitic capacitorformed among the metal lines of the spiral inductor 10 and C_(P) denotesa parasitic capacitance of a parasitic capacitor formed between thespiral inductor 10 and a silicon substrate. The parasitic capacitanceC_(P) is calculated from the thickness of an insulating layer formedbetween the spiral inductor 10 and the silicon substrate. Referencecharacter R_(P) denotes modeling of an ultra radio frequency leakageeffect.

[0013] The entire quality factor Q of the equivalent circuit shown inFIG. 1 is calculated using Equation 1: $\begin{matrix}{{Q({qualityfactor})} = \frac{{{MagneticEnergy}({Em})} - {{ElectricEnergy}({Ee})}}{{EnergyLoss}({Eloss})}} & (1)\end{matrix}$

[0014] wherein the magnetic energy (Em), the electric energy (Ee), andthe energy loss (Eloss) are calculated using Equations 2, 3, and 4,respectively: $\begin{matrix}{{Em} = \frac{V^{2}\varpi \quad {Ls}}{2\left\lbrack {\left( {\varpi \quad {Ls}} \right)^{2} + {Rs}^{2}} \right\rbrack}} & (2) \\{{Ee} = \frac{V^{2}{\varpi \left( {{Cs} + {Cp}} \right)}}{2}} & (3) \\{{Eloss} = {\frac{V^{2}}{2}\left\lbrack {\frac{1}{Rp} + \frac{Rs}{\left( {\varpi \quad {Ls}} \right)^{2} + {Rs}^{2}}} \right\rbrack}} & (4)\end{matrix}$

[0015] As may be seen in Equations 2, 3, and 4, as the conductorresistance R_(S) and the parasitic capacitances C_(S) and C_(P) of theparasitic capacitors formed by coupling decrease, the magnetic energy(Em) increases, and the electric energy (Ee) and the energy loss (Eloss)decrease. Referring to Equation 1, in this case, the quality factor Qincreases.

[0016]FIG. 2 illustrates an inductor having a horizontal multi-layerstructure of the prior art. In FIG. 2, reference numeral 100 denotes asubstrate, reference numerals 101 and 102 denote interlayer insulatinglayers, and reference character 1A denotes a lead wiring connected tofirst conductive layer patterns 1.

[0017] In the inductor shown in FIG. 2, the first conductive layerpatterns 1 are connected to second conductive layer patterns 2 viacontact holes 3. Thus, the thickness of the entire conductive layerconstituting the inductor is increased, which reduces a resistance R_(S)of the conductive layer. In addition, since a lead wiring 2A is formedunder the first conductive layer patterns 1, the number of conductivelayers is reduced. The lead wiring 2A is connected to one of the firstconductive layer patterns 1 via a lead contact hole 3A.

[0018]FIG. 3 illustrates a spiral inductor having a vertical multi-layerstructure of the prior art, which was proposed to overcome the limits ofa planar structure. In FIG. 3, reference numerals 201, 205, and 207denote first, second and third single loop type inductors, respectively.Reference numerals 202 and 203 denote an outer end and inner end of thefirst single loop type inductor 201, respectively. Reference numeral 204denotes an inner end of the second single loop type inductor 205. Theinner end 203 of the first single loop type inductor 201 is connected tothe inner end 204 of the second single loop type inductor 205 via across contact 206. Reference numeral 208 denotes a vertical directioncontact via connecting the second single loop type inductor 205 to thethird single loop type inductor 207.

[0019] As described above, in an inductor according to the prior art, asthe thickness of metal layers increases, it may be possible to expectthe effect that the quality factor Q of the inductor increases. However,because of couplings between the metal layers and between the firstmetal layer (bottom metal layer) and the silicon substrate of theinductor of the prior art, the quality factor Q and inductance of theinductor may be reduced, and the frequency range available for theinductor may be limited.

SUMMARY OF THE INVENTION

[0020] In an effort to solve these and other problems, an inductorhaving a high quality factor Q and occupying a small area in an RFIC isprovided.

[0021] According to a feature of an embodiment of the present invention,there is provided an inductor including a plurality of unit inductorseach having a vertical spiral structure, wherein a verticalcross-section of at least one unit inductor selected from the pluralityof unit inductors is an inverted trapezoid.

[0022] In the inductor above, a vertical cross-section of the remainingunit inductors may have an inverted trapezoid structure. Alternatively,the vertical cross-section of the remaining unit inductors may have aninverted trapezoid, circular, triangular, rectangular, or ellipticalstructure.

[0023] It is preferable that each unit inductor of the plurality of unitinductors has a same size. However, one unit inductor selected from theplurality of unit inductors may have a size that is different from thatof the rest.

[0024] In an embodiment of the present invention, the at least one unitinductor selected from the plurality of unit inductors includesmulti-layer metal layers and conductive plugs that vertically connectthe multi-layer metal layers, wherein each layer of the multi-layermetal layers formed between a top layer of the multi-layer metal layersand a bottom layer of the multi-layer metal layers includes two metallayers, and metal layers of the multi-layer metal layers formed underthe top layer of the multi-layer metal layers do not overlap except atportions thereof connected via the conductive plugs. The metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers are preferably symmetrical. The top layer ofthe multi-layer metal layers is preferably connected to a metal layerunder a top layer of a unit inductor adjacent to the selected unitinductor.

[0025] In an embodiment of the present invention, metal layers formed onat least one layer of the multi-layer metal layers formed between thetop layer of the multi-layer metal layers and the bottom layer of themulti-layer metal layers have a same length, thickness, and width.However, at least one of a length, thickness, and width of metal layersformed on at least one layer of the multi-layer metal layers formedbetween the top layer of the multi-layer metal layers and the bottomlayer of the multi-layer metal layers may be different from a respectivelength, thickness, and width of the others. Alternatively, metal layersformed between the top layer of the multi-layer metal layers and thebottom layer of the multi-layer metal layers may have a same length,thickness, and width. However, at least one of a length, thickness, andwidth of metal layers formed on different layers of the multi-layermetal layers formed between the top layer of the multi-layer metallayers and the bottom layer of the multi-layer metal layers is differentfrom a respective length, thickness, and width of the others.

[0026] Preferably, the conductive plugs have the same length. However,conductive plugs on different layers may have different lengths.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The above and other features and advantages of the presentinvention will become more apparent by describing in detail exemplaryembodiments thereof with reference to the attached drawings in which:

[0028]FIG. 1 illustrates a perspective view and an equivalent circuitdiagram of a general inductor used in an RFIC according to the priorart;

[0029]FIG. 2 illustrates a cross-sectional view of an inductor used inan RFIC according to the prior art;

[0030]FIG. 3 illustrates a plane view of an inductor used in an RFICaccording to different prior art;

[0031]FIG. 4 illustrates a perspective view of a first inductor used inan RFIC according to a first embodiment of the present invention;

[0032]FIGS. 5 and 6 illustrate vertical cross-sectional views of firstand second unit inductors included in the first inductor shown in FIG.4;

[0033]FIG. 7 illustrates a perspective view of a second inductor used inan RFIC according to a second embodiment of the present invention;

[0034]FIGS. 8 through 10 illustrate vertical cross-sectional views ofthird through fifth unit inductors included in the second inductor shownin FIG. 7;

[0035]FIG. 11 illustrates a three-dimensional structure of the firstinductor according to the first embodiment of the present invention,which was used in a simulation carried out for comparing the presentinvention with the prior art; and

[0036]FIG. 12 is a graph illustrating results of a simulation carriedout for comparing the first and second inductors according to the firstand second embodiments of the present invention with an inductoraccording to the prior art.

DETAILED DESCRIPTION OF THE INVENTION

[0037] Korean Patent Application No. 2002-55634, filed on Sep. 13, 2002,and entitled: “Inductor For Radio Frequency Integrated Circuit,” isincorporated by reference herein in its entirety.

[0038] An inductor used in an RFIC, according to embodiments of thepresent invention, will be described more fully hereinafter withreference to the accompanying drawings, in which preferred embodimentsof the invention are shown. The invention may, however, be embodied indifferent forms and should not be construed as limited to theembodiments set forth herein. Rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. In thedrawings, the thicknesses of layers or regions are exaggerated forclarity, and like numbers refer to like elements throughout.

[0039] An inductor according to an embodiment of the present inventionsolves disadvantages of a conventional inductor having a horizontalstructure. An inductor according to an embodiment of the presentinvention may be characterized in that multi-layer metal layers stackedon a substrate are interconnected through via holes and geometricalforms of unit inductors have an inverted trapezoid structure, and theunit inductors are horizontally connected in a spiral form.

First Embodiment

[0040]FIG. 4 illustrates a perspective view of a first inductor used inan RFIC according to a first embodiment of the present invention. Afirst inductor according to a first embodiment of the present inventionincludes a plurality of unit inductors, each having an invertedtrapezoid structure and a same size.

[0041] In particular, referring to FIG. 4, a first inductor D1 includesfirst, second, and third unit inductors D1 a, D1 b, and D1 c,respectively, which are horizontally connected in a spiral form. Ifnecessary, the first inductor D1 may include additional unit inductors.Each of the first, second, and third unit inductors D1 a, D1 b, and D1 chas an inverted trapezoid structure, and is formed of multi-layer metallayers, arranged such that distances between the metal layers in eachlayer of metal layers increase in an upward direction along the unitinductor.

[0042] For example, although not illustrated, if a layer of metallayers, x, for example, is positioned above any other layer of metallayers, x-n, for example, then a distance between the metal layers inthe layer of metal layers x is greater than a distance between the metallayers in the layer of metal layers x-n, which is positioned below thelayer of metal layers x. Also, metal layers in a layer of metal layersare vertically connected to metal layers in another layer of metallayers through via holes. Thus, in a unit inductor, portions thereofconnecting a bottom metal layer to a top metal layer form a stairpattern. In addition, it is preferable that the thickness and width ofthe metal layers in each layer of metal layers are uniform.

[0043] Referring again to FIG. 4, a sixth metal layer 74 of one of thefirst, second, and third unit inductors D1 a, D1 b, and D1 c, e.g., thesecond unit inductor D1 b, is connected to a fifth metal layer 68 a ofan adjacent unit inductor, i.e., the first unit inductor D1 a. Here, thefifth metal layer 68 a of the first unit inductor D1 a is connected tothe sixth metal layer 74 of the second unit inductor D1 b via aconductive plug 72 filling a via hole (not shown). As shown in FIG. 4,the first, second, and third unit inductors D1 a, D1 b, and D1 c arehorizontally arranged linearly with a predetermined distancetherebetween. Thus, in order to connect the fifth metal layer 68 a ofthe first unit inductor D1 a to the sixth metal layer 74 of the secondunit inductor D1 b as described above, the sixth metal layer 74 of thesecond unit inductor D1 b extends a predetermine distance toward thefifth metal layer 68 a of the first unit inductor D1 a. The fifth metallayer 68 a of the first unit inductor D1 a also extends the samedistance toward the sixth metal layer 74 of the second unit inductor D1b. The extending portion of the sixth metal layer 74 of the second unitinductor D1 b is connected to the extending portion of the fifth metallayer 68 a of the first unit inductor D1 a via the conductive plug 72.As a result, the sixth metal layer 74 of the second unit inductor D1 bis connected to the fifth metal layer 68 a of the first unit inductor D1a within a space between the first and second unit inductors D1 a and D1b. This connection structure is also applied to the connection of thesecond and third unit inductors D1 b and D1 c.

[0044] Insulating layers (not shown) are formed in-between the first,second, and third unit inductors D1 a, D1 b, and D1 c, and enclose themetal layers constituting the first, second, and third unit inductors D1a, D1 b, and D1 c and conductive plugs connecting the metal layers,which will be explained in greater detail later.

[0045] Vertical cross-sectional structures of the first, second, andthird unit inductors D1 a, D1 b, and D1 c will now be described.However, because the first, second, and third unit inductors D1 a, D1 b,and D1 c have the same structure, only the vertical cross-sectionalstructures of the first and second unit inductors D1 a and D1 b will bedescribed.

[0046] First, the vertical cross-sectional structure of the first unitinductor D1 a will be explained.

[0047] Referring to FIG. 5, an insulating layer 42 is formed on asubstrate 40, e.g., a silicon substrate. The insulating layer 42 is, forexample, a silicon oxide layer which increases a gap between thesubstrate 40 and an inductor formed on the substrate 40 in order toreduce coupling of the inductor to the substrate 40. A first metal layer44 is formed in a predetermined area of the insulating layer 42. A firstinterlayer insulating layer 46 is formed on the insulating layer 42 tocover the first metal layer 44. First via holes h1 are formed in thefirst insulating layer 46 to expose portions of outer ends of the firstmetal layer 44, and are filled with first conductive plugs 48. It ispreferable that the first conductive plugs 48 are formed of the samematerial as the first metal layer 44 in order to minimize contactresistance between the first metal layer 44 and second metal layers 50formed over the first metal layer 44. If the first metal layer 44 andthe second metal layers 50 are formed of different materials, anotherconductive material may be interposed between the first conductive plugs48 and the first metal layer 44 and/or the first conductive plugs 48 andthe second metal layers 50. This may be applied to metal layers 56, 62,68, and 74 formed over the second metal layers 50, and to conductiveplugs 54, 60, 66, 68 a, and 72 connecting the metal layers 56, 62, 68,and 74 as well as to conductive plugs connecting metal layersconstituting a second inductor that will be described in detail in asecond embodiment.

[0048] The second metal layers 50, which contact the first conductiveplugs 48, are formed on the first interlayer insulating layer 46 aboveportions of both ends of the first metal layer 44. The second metallayers 50 are formed over the first conductive plugs 48, and extendoutwardly beyond both ends of the first metal layer 44. In other words,the second metal layers 50 are symmetrically formed to be centeredaround and above the first metal layer 44, overlapping portions of bothends of the first metal layer 44, thereby contacting the firstconductive plugs 48, and extending beyond both ends of the first metallayer 44. As a result, the distance between inner, facing ends of thesecond metal layers 50 is shorter than the distance between both ends ofthe first metal layer 44, while the distance between outer ends of thesecond metal layers 50 is longer than the distance between both ends ofthe first metal layer 44.

[0049] A second interlayer insulating layer 52 is formed on the firstinterlayer insulating layer 46 to cover the second metal layers 50.Second via holes h2 are formed in the second interlayer insulating layer52 to expose portions of outer ends of the second metal layers 50 andare filled with second conductive plugs 54. Third metal layers 56 areformed on predetermined areas of the second interlayer insulating layer52 to have a predetermined distance therebetween, and to contact thesecond conductive plugs 54. The third metal layers 56 are formed underthe same conditions as the second metal layers 50 and contact the secondconductive plugs 54 under the same conditions that the second metallayers 50 contact the first conductive plugs 48, so that a distancebetween inner, facing ends of the third metal layers 56 is longer thanthe distance between the inner, facing ends of the second metal layers50 and shorter than the distance between the outer ends of the secondmetal layers 50. The distance between outer ends of the third metallayers 56 is much greater than the distance between the outer ends ofthe second metal layers 50. Also, the third metal layers 56 aresymmetrically formed to be centered around and above the first metallayer 44.

[0050] A third interlayer insulating layer 58 is formed on the secondinterlayer insulating layer 52 to cover the third metal layers 56. Thirdvia holes h3 are formed in the third interlayer insulating layer 58 toexpose portions of outer ends of the third metal layers 56, and arefilled with third conductive plugs 60. The third via holes h3, andtherefore the third conductive plugs 60, are spaced farther apart thanthe second via holes h2 and the second conductive plugs 54.

[0051] Fourth metal layers 62 are formed on predetermined areas of thethird interlayer insulating layer 58 to have a predetermined distancetherebetween, and to contact the third conductive plugs 60. The fourthmetal layers 62 are formed under the same conditions as the third metallayers 56, and contact the third conductive plugs 60 under the sameconditions that the third metal layers 56 contact the second conductiveplugs 54, so that a distance between inner, facing ends of the fourthmetal layers 62 is longer than the distance between the inner, facingends of the third metal layers 56 and shorter than the distance betweenthe outer ends of the third metal layers 56. The fourth metal layers 62are also symmetrically formed to be centered around and above the firstmetal layer 44. Preferably, the second, third, and fourth metal layers50, 56, and 62 have the same thickness and length.

[0052] As described above, since the distance between metal layersformed over the first metal layer 44 gets longer in an upward directionalong a unit inductor, metal layers in upper positions do not overlapmetal layers in lower positions except at portions thereof connected viathe conductive plugs. As a result, a parasitic capacitance due tocoupling among metal layers in an inductor having a vertical structuremay be prevented.

[0053] A fourth interlayer insulating layer 64 is formed on the thirdinterlayer insulating layer 58 to cover the fourth metal layers 62.Fourth via holes h4 are formed in the fourth interlayer insulating layer64 to expose portions of outer ends of the fourth metal layers 62, and adistance between the fourth via holes h4 is longer than the distancebetween the third via holes h3. The fourth via holes h4 are filled withfourth conductive plugs 66. Fifth metal layers 68 and 68 a are formed onpredetermined areas of the fourth interlayer insulating layer 64including the fourth conductive plugs 66, and are formed to besymmetrical to the first metal layer 44. A distance between the fifthmetal layers 68 and 68 a is greater than the distance between the fourthmetal layers 62. The fifth metal layers 68 and 68 a and the fourth metallayers 62 are connected via the fourth conductive plugs 66.

[0054] The fifth metal layer 68 a on a right side of the first unitinductor D1 a is connected to the second unit inductor D1 b, as will bedescribed later with reference to FIG. 6. The fifth metal layer 68 a mayhave the same thickness and length as the fifth metal layer 68 on a leftside of the first unit inductor D1 a. A fifth interlayer insulatinglayer 70 is formed on the fourth interlayer insulating layer 64 to coverthe fifth metal layers 68 and 68 a. A fifth via hole h5 is formed in thefifth interlayer insulating layer 70 to expose a portion of an outer endof the fifth metal layer 68 on the left side of the first unit inductorD1 a and is filled with a fifth conductive plug 72.

[0055] A sixth metal layer 74 is formed on the fifth interlayerinsulating layer 70 to be connected to the fifth conductive plug 72. Anend of the sixth metal layer 74 is formed over the fifth conductive plug72, and the sixth metal layer 74 is formed to have a lengthcorresponding to a distance between outer ends of the fifth metal layers68 and 68 a. A sixth interlayer insulating layer 76 is formed around thesixth metal layer 74 on the fifth interlayer insulating layer 70.

[0056] As described above, the first unit inductor D1 a is composed ofthe first, second, third, fourth, fifth, and sixth metal layers 44, 50,56, 62, 68 and 68 a, and 74, respectively, and the first, second, third,fourth, and fifth conductive plugs 48, 54, 60, 66, and 72. Thus, thefirst unit inductor D1 a has an inverted trapezoid structure with sidesthat correspond to stairs, which are symmetrical with respect to thefirst metal layer 44. As a result, coupling between the substrate 40 andthe first, second, third, fourth, fifth, and sixth metal layers 44, 50,56, 62, 68 and 68 a, and 74, is reduced.

[0057] The first unit inductor D1 a is shown in FIG. 5 having aninverted trapezoid structure. However, the first unit inductor D1 a isnot limited to having a structure of an inverted trapezoid, but may betriangular, rectangular, circular, or elliptical. In this case, it ispreferable that the first unit inductor D1 a is formed so thatoverlapping areas of metal layers are minimized to minimize couplingamong the metal layers.

[0058]FIG. 6 illustrates a cross-sectional view of the second unitinductor D1 b of FIG. 4. Here, the second unit inductor D1 b has thesame structure and shape as the first unit inductor D1 a shown in FIG. 5except that an additional fifth via hole h5 is formed in the fifthinterlayer insulating layer 70 at a right side of the second unitinductor D1 b, and is filled with a conductive plug 72 a. The conductiveplug 72 a is formed between a fifth metal layer 68 a and a sixth metallayer 74 to thereby connect the fifth metal layer 68 a and the sixthmetal layer 74. The conductive plug 72 a is formed with the fifthconductive plug 72. As previously mentioned, the conductive plug 72 aalso connects the sixth metal layer 74 of the second unit inductor D1 bto the fifth metal layer 68 a of the first unit inductor D1 a within aspace between the first and second unit inductors D1 a and D1 b.

Second Embodiment

[0059] In the second embodiment of the present invention, unit inductorsare formed to have different sizes and are arranged according to thesizes thereof to minimize effects between metal layers and a substrate,as well as between metal layers of adjacent unit inductors.

[0060] Referring to FIG. 7, a second inductor D2 having a verticalspiral structure includes fourth, fifth, and sixth unit inductors D2 a,D2 b, and D2 c, which each have an inverted trapezoid structure and arespirally arranged in a horizontal direction. However, the fifth unitinductor D2 b is smaller than the fourth and sixth unit inductors D2 aand D2 c. Thus, a fifth metal layer 68 b of the fifth unit inductor D2 bis connected to a fourth metal layer 62 of the fourth unit inductor D2 avia a fourth conductive plug 66 and a fifth metal layer 67 of the fourthunit inductor D2 a. A fourth metal layer 62 a of the fifth unit inductorD2 b is connected to a sixth metal layer 74 b of the sixth unit inductorD2 c via a fourth conductive plug 66 b, a fifth metal layer 68 c, and afifth conductive plug 72 a within a space between the fifth unitinductor D2 b and the sixth unit inductor D2 c.

[0061] Vertical cross-sectional structures of the fourth, fifth, andsixth unit inductors D2 a, D2 b, and D2 c will now be described,beginning with the vertical cross-sectional structure of the fourth unitinductor D2 a.

[0062] Referring to FIG. 8, an insulating layer 42 is formed on asubstrate 40, and a first metal layer 44 is formed on a predeterminedarea of the insulating layer 42. A first interlayer insulating layer 46is formed on the insulating layer 42 to cover the first metal layer 44.First via holes h1 are formed in the first interlayer insulating layer46 to have a predetermined distance d therebetween, thereby exposingportions of both outer ends of the first metal layer 44. The verticalcross-sectional structure from a second interlayer insulating layer 52to a fourth interlayer insulating layer 64 is the same as that describedin the first embodiment, and thus will not be explained herein.

[0063] A fifth metal layer 68 is formed on the fourth interlayerinsulating layer 64. A portion of right end of the fifth metal layer 68contacts a fourth conductive plug 66 filling a fourth via hole h4 formedin the fourth interlayer insulating layer 64 at a left side of thefourth unit inductor D2 a. A fourth via hole h4 is also formed in thefourth interlayer insulating layer 64 at a right side of the fourth unitinductor D2 a to expose a portion of a right most end of fourth metallayers 62, and is filled with a fourth conductive plug 66. A fifthinterlayer insulating layer 70 is formed on the fourth interlayerinsulating layer 64 to cover the fifth metal layer 68. A fifth via holeh5 is formed in the fifth interlayer insulating layer 70 to expose aportion of a left end of the fifth metal layer 68, and is filled withfifth conductive plug 72. A sixth metal layer 74 a is formed on thefifth interlayer insulating layer 70 to contact the fifth conductiveplug 72, and to extend past a right most end of the fourth conductiveplugs 66. A sixth interlayer insulating layer 76 is formed around thesixth metal layer 74 a. The fourth unit inductor D2 a is connected tothe fifth unit inductor D2 b via the fourth conductive plugs 66.

[0064] A vertical cross-sectional view of the fifth unit inductor D2 b,which is smaller than the fourth and sixth unit inductors D2 a and D2 c,will now be described.

[0065] Referring to FIG. 9, a second metal layer 50 a is formed on afirst interlayer insulating layer 46. Here, a position in which thesecond metal layer 50 a is formed corresponds to a space between thesecond metal layers 50 of the fourth unit inductor D2 a of FIG. 8, andsimilarly to a space between second metal layers of the sixth unitinductor D2 c. It is preferable that a length d1 of the second metallayer 50 a is shorter than the distance d between the first conductiveplugs 48 connecting the first metal layer 44 to the second metal layers50 of the fourth unit inductor D2 a shown in FIG. 8. A second interlayerinsulating layer 52 is formed on the first interlayer insulating layer46 to cover the second metal layer 50 a. Second via holes h2 a areformed in the second interlayer insulating layer 52 to expose portionsof outer ends of the second metal layer 50 a and are filled with secondconductive plugs 54 a. Third metal layers 56 a are formed on the secondinterlayer insulating layer 52 to have a predetermined distancetherebetween. Portions of inner ends of the third metal layers 56 a arerespectively connected to second conductive plugs 54 a. The distancebetween the third metal layers 56 a is shorter than the length d1 of thesecond metal layer 50 a while the distance between outer ends of thethird metal layers 56 a is much longer than the length d1 of the secondmetal layer 50 a. However, it is preferable that the distance betweenouter ends of the third metal layers 56 a is shorter than the distancebetween the third metal layers 56 of the fourth and fifth unit inductorsD2 a and D2 c of FIGS. 8 and 10. Accordingly, it is possible to preventmetal layers formed on an insulating layer of the fifth unit inductor D2b from being arranged too closely to metal layers of the fourth andsixth unit inductors D2 a and D2 c. As a result, horizontal couplingamong adjacent unit inductors may be minimized.

[0066] A third interlayer insulating layer 58 is formed on the secondinterlayer insulating layer 52 to cover the third metal layers 56 a.Third via holes h3 a are formed in the third interlayer insulating layer58 to expose portions of outer ends of the third metal layers 56 a.Thus, a distance between the third via holes h3 a is much longer thanthe distance between the second via holes h2 a and smaller than thedistance between the third metal layers 56 of the fourth and fifth unitinductors D2 a and D2 c of FIGS. 8 and 10. The third via holes h3 a arefilled with third conductive plugs 60 a. Fourth metal layers 62 a areformed on the third interlayer insulating layer 58 to have apredetermined distance therebetween, and portions of inner ends thereofare connected to the third conductive plugs 60 a. It is preferable thata distance between outer ends of the fourth metal layers 62 a is shorterthan the distance between the fourth metal layers 62 of the fourth andsixth unit inductors D2 a and D2 c of FIGS. 8 and 10. The fourth metallayer 62 a on a right side of the fifth unit inductor D2 b is connectedto a sixth metal layer 74 b of the sixth unit inductor D2 c shown inFIG. 10. A fourth interlayer insulating layer 64 is formed on the thirdinterlayer insulating layer 58 to cover the fourth metal layers 62 a. Afourth via hole h4 a is formed in the fourth interlayer insulating layer64 to expose a portion of a left most end of the fourth metal layers 62a on a left side of the fifth unit inductor D2 b, and is filled with afourth conductive plug 66 a. A fifth metal layer 68 b is formed on thefourth interlayer insulating layer 64 to be connected to the fourthconductive plug h4 a, and to extend a predetermined distance to theright of the fourth conductive plug h4 a. It is preferable that a lengthof the fifth metal layer 68 b is shorter than the distance between thefourth via holes h4 of the fourth and sixth unit inductors D2 a and D2 cof FIGS. 8 and 10.

[0067] As indicated by dotted lines in FIG. 9, a fourth metal layer 62of the fourth unit inductor D2 a is formed on the third interlayerinsulating layer 58 to be connected to the fifth metal layer 68 b of thefifth unit inductor D2 b. The fourth metal layer 62 of the fourth unitinductor D2 a and the fifth metal layer 68 b of the fifth unit inductorD2 b are connected via the fourth conductive plug 66 filling the fourthvia hole h4 through which a portion of the right most end of the fourthmetal layers 62 is exposed in the fourth unit inductor D2 a.

[0068] A fifth interlayer insulating layer 70 is formed on the fourthinterlayer insulating layer 64 to cover the fifth metal layer 68 b, anda sixth interlayer insulating layer 76 is formed on the fifth interlayerinsulating layer 70.

[0069] The vertical cross-sectional structure of the sixth unit inductorD2 c will now be described with reference to FIG. 10.

[0070] As shown in FIG. 10, the vertical cross-sectional structure ofthe sixth unit inductor D2 c from a substrate 40 to fourth conductiveplugs 66 is the same as that of the fourth unit inductor D2 a shown inFIG. 8, and thus will not be described herein.

[0071] Referring to FIG. 10, a fifth metal layer 68 is formed on thefourth interlayer insulating layer 64 to be connected to the fourthconductive plug 66 on a left side of the sixth unit inductor D2 c. Afifth interlayer insulating layer 70 is formed on the fourth interlayerinsulating layer 64 to cover the fifth metal layer 68. A fifth via holeh5 is formed in the fifth interlayer insulating layer 70 to expose aportion of a left end of the fifth metal layer 68 and is filled with afifth conductive plug 72. A sixth metal layer 74 b is formed on thefifth interlayer insulating layer 70 to be connected to the fifthconductive plug 72. The sixth metal layer 74 b extends beyond the fourthvia holes h4 and is connected at a right end thereof to the fourth metallayer 62 a of the fifth unit inductor D2 b of FIG. 9.

[0072] Since the second inductor according to the second embodiment ofthe present invention includes unit inductors having different sizes,coupling of metal layers to the substrate 40 is reduced further than inthe first embodiment.

[0073] Both the first inductor and the second inductor according to thefirst and second embodiments of the present invention have a lowercapacitance (C_(P)) and ultra radio frequency (R_(P)) than an inductoraccording to the prior art. Therefore, a quality factor Q of an inductoraccording to the present invention may be higher than that of aninductor according to the prior art. Also, in the second inductoraccording to the second embodiment of the present invention, small areasof unit inductors overlap horizontally, and thus a parasitic capacitanceC_(S) is reduced. As a result, the electric energy (Ee) and the energyloss (Eloss) of the second inductor may be reduced, which increases thequality factor Q thereof.

[0074] In order to verify characteristics of the first and secondinductors according to the present invention, the inventor of thepresent invention carried out a simulation for analyzingthree-dimensional structures of the first and second inductors accordingto the first and second embodiments of the present invention and thehorizontal spiral inductor shown in FIG. 1 under similar conditions, andcompared quality factors of the first and second inductors according tothe present invention with a quality factor of the inductor according tothe prior art.

[0075] In the simulation described above, a width of metal layersconstituting an inductor was set to 3 μm, a gap among turns of the metallayers was set to 4 μm, a thickness of the metal layers was set to 1 μm,and a total length of the metal layers was set to 230 μm.

[0076]FIG. 11 illustrates the three-dimensional structure of the firstinductor according to the first embodiment of the present invention usedin the simulation described above, and FIG. 12 is a graph illustratingthe results of the simulation.

[0077] In FIG. 12, first and second graphs G1 and G2 illustrate resultsof the simulation obtained using the first and second inductors of thepresent invention, respectively, and third graph G3 illustrates resultsof the simulation obtained using the inductor shown in FIG. 1.

[0078] As may be seen in the first, second, and third line graphs G1,G2, and G3, a quality factor Q increases with an increase in frequency.At a same frequency, the second inductor according to the presentinvention has the highest quality factor Q, the first inductor has thesecond highest quality factor Q, and the inductor shown in FIG. 1 hasthe lowest quality factor Q.

[0079] The first and second inductors according to the present inventionhave an area of about 25×34 μm² and the inductor shown in FIG. 1 has anarea of about 39×36 μm². Thus, areas of the first and second inductorsaccording to the present invention are smaller than that of the inductorof the prior art shown in FIG. 1.

[0080] As described above, since an inductor according to embodiments ofthe present invention can be formed using a CMOS process ofsemiconductor manufacturing processes, an additional process is notrequired. Further, by minimizing parasitic components caused by couplingof an inductor to a substrate and by vertical and horizontal couplingamong metal layers of the inductor, the quality factor of the inductormay be increased, thereby increasing the range of inductor device fieldsin which inductors of the present invention may be used.

[0081] Although a number of times metal layers of inductors according tothe present invention are wound is the same as that of a horizontalmulti-layer inductor according to the prior art, the horizontal area onwhich inductors of the present invention may be formed is smaller thanthat of the horizontal multi-layer inductor of the prior art. Moreover,as gate lengths are reduced and a number of stacked metal layers isincreased due to developments in semiconductor manufacturing processes,an inductance of an inductor according to the present invention may befurther increased.

[0082] Preferred embodiments of the present invention have beendisclosed herein and, although specific terms are employed, they areused and are to be interpreted in a generic and descriptive sense onlyand not for purpose of limitation. Accordingly, it will be understood bythose of ordinary skill in the art that various changes in form anddetails may be made without departing from the spirit and scope of thepresent invention as set forth in the following claims.

[0083] For example, it will be understood by those of ordinary skill inthe art that lengths of metal layers of the first or second inductoraccording to first and second embodiments of the present invention maybe different for each layer. Also, unit inductors of the second inductormay be formed in different shapes. For example, a fourth unit inductormay be an inverted trapezoid, a fifth unit inductor may be triangular,and a sixth unit inductor may be circular, rectangular, or elliptical.In addition, an inductor having a new structure may be formed bycombining inductor structures proposed in the present invention and anexisting inductor structure.

What is claimed is:
 1. An inductor comprising a plurality of unitinductors each having a vertical spiral structure, wherein a verticalcross-section of at least one unit inductor selected from the pluralityof unit inductors is an inverted trapezoid.
 2. The inductor as claimedin claim 1, wherein a vertical cross-section of the remaining unitinductors has an inverted trapezoid structure.
 3. The inductor asclaimed in claim 1, wherein a vertical cross-section of the remainingunit inductors has an inverted trapezoid, circular, triangular,rectangular, or elliptical structure.
 4. The inductor as claimed inclaim 2, wherein each unit inductor of the plurality of unit inductorshas a same size.
 5. The inductor as claimed in claim 2, wherein one unitinductor selected from the plurality of unit inductors has a size thatis different from that of the rest.
 6. The inductor as claimed in claim1, wherein the at least one unit inductor selected from the plurality ofunit inductors comprises: multi-layer metal layers; and conductive plugsthat vertically connect the multi-layer metal layers, wherein layers ofthe multi-layer metal layers formed between top and bottom layers of themulti-layer metal layers include two metal layers, and metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers do not overlap except at portions thereofconnected via the conductive plugs.
 7. The inductor as claimed in claim6, wherein the metal layers of the multi-layer metal layers formed underthe top layer of the multi-layer metal layers are symmetrical.
 8. Theinductor as claimed in claim 6, wherein the top layer of the metallayers is connected to a metal layer under a top layer of a unitinductor adjacent to the selected unit inductor.
 9. The inductor asclaimed in claim 6, wherein metal layers formed on at least one layer ofthe multi-layer metal layers formed between the top layer of themulti-layer metal layers and the bottom layer of the multi-layer metallayers have a same length, thickness, and width.
 10. The inductor asclaimed in claim 6, wherein at least one of a length, thickness, andwidth of metal layers formed on at least one layer of the multi-layermetal layers formed between the top layer of the multi-layer metallayers and the bottom layer of the multi-layer metal layers is differentfrom a respective length, thickness, and width of the others.
 11. Theinductor as claimed in claim 7, wherein metal layers formed between thetop layer of the multi-layer metal layers and the bottom layer of themulti-layer metal layers have a same length, thickness, and width. 12.The inductor as claimed in claim 7, wherein at least one of a length,thickness, and width of metal layers formed on different layers betweenthe top layer of the multi-layer metal layers and the bottom layer ofthe multi-layer metal layers is different from a respective length,thickness, and width of the others.
 13. The inductor as claimed in claim6, wherein the conductive plugs have the same length.
 14. The inductoras claimed in claim 6, wherein conductive plugs on different layers havedifferent lengths.
 15. The inductor as claimed in claim 2, wherein theat least one unit inductor selected from the plurality of unit inductorscomprises: multi-layer metal layers; and conductive plugs thatvertically connect the multi-layer metal layers, wherein layers of themulti-layer metal layers formed between top and bottom layers of themulti-layer metal layers include two metal layers, and metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers do not overlap except at portions thereofconnected via the conductive plugs.
 16. The inductor as claimed in claim3, wherein the at least one unit inductor selected from the plurality ofunit inductors comprises: multi-layer metal layers; and conductive plugsthat vertically connect the multi-layer metal layers, wherein layers ofthe multi-layer metal layers formed between top and bottom layers of themulti-layer metal layers include two metal layers, and metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers do not overlap except at portions thereofconnected via the conductive plugs.
 17. The inductor as claimed in claim4, wherein the at least one unit inductor selected from the plurality ofunit inductors comprises: multi-layer metal layers; and conductive plugsthat vertically connect the multi-layer metal layers, wherein layers ofthe multi-layer metal layers formed between top and bottom layers of themulti-layer metal layers include two metal layers, and metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers do not overlap except at portions thereofconnected via the conductive plugs.
 18. The inductor as claimed in claim5, wherein the at least one unit inductor selected from the plurality ofunit inductors comprises: multi-layer metal layers; and conductive plugsthat vertically connect the multi-layer metal layers, wherein layers ofthe multi-layer metal layers formed between top and bottom layers of themulti-layer metal layers include two metal layers, and metal layers ofthe multi-layer metal layers formed under the top layer of themulti-layer metal layers do not overlap except at portions thereofconnected via the conductive plugs.